Journal of Global Optimization

, Volume 57, Issue 1, pp 251–277 | Cite as

Welfare-maximizing correlated equilibria using Kantorovich polynomials with sparsity

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Abstract

We provide motivations for the correlated equilibrium solution concept from the game-theoretic and optimization perspectives. We then propose an algorithm that computes \({\varepsilon}\) -correlated equilibria with global-optimal (i.e., maximum) expected social welfare for normal form polynomial games. We derive an infinite dimensional formulation of \({\varepsilon}\) -correlated equilibria using Kantorovich polynomials, and re-express it as a polynomial positivity constraint. We exploit polynomial sparsity to achieve a leaner problem formulation involving sum-of-squares constraints. By solving a sequence of semidefinite programming relaxations of the problem, our algorithm converges to a global-optimal \({\varepsilon}\) -correlated equilibrium. The paper ends with two numerical examples involving a two-player polynomial game, and a wireless game with two mutually-interfering communication links.

Keywords

Game theory Non-cooperative game Correlated equilibrium Global polynomial optimization Sum of squares Semidefinite programming Wireless communication 

Mathematics Subject Classification

91A10 91A80 90C22 11E25 90B18 

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Copyright information

© Springer Science+Business Media, LLC. 2012

Authors and Affiliations

  1. 1.Department of ComputingImperial CollegeLondonUK

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